Reinforcement learning for robotic motion planning - Problem statement ideas
I think that this may be too difficult for only a few weeks of work. There are a few reasons why and although all of the reasons are themselves learning opportunities, it may cost you more time than you have. 

First off, Robots are hard to work with. Ask anyone who has worked with robots and they will say that have broken their heart at least once. This is because either the robot was a custom robot which needs specific skills (soldering, 3d printing, etc) if something breaks (and it will) or it's a purchased robot platform which doesn't have the control you want or doesn't have good documentation. 

Secondly, Machine learning is a very interesting and broad field and there is a lot of literature one should get a background on to help with their projects. Because of this, it might be overwhelming to take all of that information in while having to deal with a robot. 

I don't want to dissuade you in this research area though. It is very interesting and has many subproblems like dynamic environments, multilevel environments, etc. But given the time you have, it might be better to set yourself up for success. Perhaps something which lets you do a literature review about the problem anyway. 
Perhaps a more attainable goal in that time while still using a robot is: Predicting wall collisions using temporal difference learning.

If you agent can predict when a wall is coming, clearly they will be able to avoid them too but it's a very reasonable first step. 

Additionally, talking to the professor of the course or your supervisor (if you have one) will also help you decide.